Calculate price elasticity of demand with midpoint, direct percentage-change, and linear demand point modes, plus absolute PED, step-by-step work.
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PED calculator
Calculate price elasticity of demand from old and new values, direct percentage changes, or a linear demand curve point. The worksheet keeps the signed PED, absolute PED, midpoint method, and total revenue effect visible where they apply.
Quick examples
Calculation mode
Formula notes
PED = % change in quantity demanded / % change in price
Use |PED| to classify elastic, inelastic, or unit elastic demand.
Midpoint percentages reduce base-period bias between old and new values.
Direct percentage mode is useful when a problem already gives the percentage changes.
Linear demand mode uses PED = (dQ / dP) x (P / Q) at one point on Q = a - bP.
Result
|PED| = 1.57
Elastic demand — quantity demanded changes more than proportionally relative to price, so total revenue usually moves opposite the price change.
The revenue test says total revenue fell by 200; based on this elasticity and price direction, revenue should fall.
Price elasticity of demand calculator guide: midpoint method, PED interpretation
A price elasticity of demand calculator estimates how responsive quantity demanded is to a price change. This page also explains the main assumptions behind the price elasticity of demand calculator result, highlights the supporting figures shown by the calculator, and helps the reader use the estimate without overstating what a quick online tool can prove.
What price elasticity of demand is measuring
Price elasticity of demand, often shortened to PED, measures the relationship between a change in price and the resulting change in quantity demanded. If quantity changes a lot when price changes a little, demand is elastic. If quantity barely moves, demand is inelastic.
Economists usually read the absolute value of PED when classifying demand because the raw number is negative on a normal demand curve. The sign still matters, though, because it shows that price and quantity moved in opposite directions.
The midpoint method and the formula
The midpoint method compares the change against the average of the old and new values instead of picking one period as the base. That reduces base-period bias and makes the result more symmetric when you compare a price increase with a price decrease.
This calculator applies the standard midpoint formula and then shows the signed PED, the absolute PED, and the percentage changes in both quantity and price so you can inspect each part of the calculation.
The midpoint method is also commonly described as arc elasticity because it measures responsiveness between two points on a demand curve rather than at one exact point.
PED = % change in quantity demanded / % change in price
The core elasticity ratio used to measure responsiveness.
Midpoint % change = (new value - old value) / average of old and new values x 100
The symmetric percentage-change method used by this calculator.
Total revenue = price x quantity
A quick check showing how the price move affected revenue in dollar terms.
Point PED for Q = a - bP: PED = -b x P / Q
The point elasticity formula used when a linear demand function and a price point are known.
Choose the right price elasticity calculator mode
Use old and new values when you have two observed price-quantity points and want the standard price elasticity of demand midpoint method. This is the safest default for textbook problems, pricing experiments, and before-and-after demand observations because it avoids changing the answer when the direction is reversed.
Use direct percentage changes when the problem already gives you a percent change in quantity demanded and a percent change in price. This mode is fastest for multiple-choice practice, quick PED checks, and interpreting a phrase such as quantity demanded fell 15 percent when price rose 10 percent.
Use the linear demand curve mode when the problem gives a demand function such as Q = a - bP and asks for point elasticity of demand at a specific price. In that case the calculator first finds quantity at the point, then applies the derivative-based formula so you can see why elasticity changes along a straight-line demand curve.
Suppose price rises from 10 to 12 while quantity demanded falls from 200 to 150. The midpoint calculation produces a PED of -1.5714 and an absolute PED of 1.5714. That is elastic demand because quantity changed more than price.
The revenue check is useful here too. Old revenue is 2,000 and new revenue is 1,800, so total revenue falls by 200. That fits the elastic-demand pattern where a price increase can reduce total revenue because the quantity loss is large enough to outweigh the higher price.
Elastic, inelastic, and unit elastic demand
Elastic demand means the absolute value of PED is greater than 1. Quantity responds more than price, so a price rise often pushes total revenue down and a price cut can raise revenue.
Inelastic demand means the absolute value is less than 1. Quantity responds less than price, so a price rise often pushes total revenue up and a price cut can reduce revenue.
Unit elastic demand means the absolute value is 1. Price and quantity move proportionally, so total revenue is at the turning point between the elastic and inelastic regions.
PED tells you how responsive buyers are, but revenue is often what you care about in a pricing decision. A seller can raise price and still lose total revenue if demand is elastic enough.
That is why this calculator shows both the elasticity result and the revenue comparison. The revenue numbers do not replace PED, but they make the practical effect of the price change easier to see.
The total revenue test is a useful interpretation layer: when demand is elastic, price and revenue usually move in opposite directions; when demand is inelastic, they usually move in the same direction. If your observed revenue change conflicts with that pattern, check whether another factor changed at the same time.
This page focuses on practical PED calculations from two observed points, direct percentage changes, or a simple linear demand function. It does not model taxes, competitor reactions, seasonal demand shifts, long-run versus short-run adjustment, or non-linear demand systems.
A result should be read as a decision aid, not as a complete demand forecast. If the underlying market is volatile or the change is large, review the assumptions before using the output in a pricing decision.
Common mistakes when calculating price elasticity of demand
Do not confuse slope with elasticity. A straight demand curve has a constant slope, but point elasticity changes along the curve because the price-to-quantity ratio changes at each point.
Do not drop the sign before you understand it. The absolute value of PED is usually used for elastic versus inelastic classification, but the signed result confirms whether quantity demanded moved in the normal opposite direction from price.
Do not enter percentage points as decimals in the direct percentage mode. Enter -15 for a 15 percent quantity decrease, not -0.15. If price change is zero, the calculator shows a warning because PED would require division by zero.
Frequently asked questions
What does price elasticity of demand measure?
It measures how much quantity demanded changes when price changes. Bigger quantity swings mean more elastic demand.
Why does the calculator use the midpoint method?
The midpoint method reduces base-period bias by comparing changes against the average of the old and new values. That makes the result symmetric for price increases and decreases.
Why is PED usually negative?
Because price and quantity demanded usually move in opposite directions on a demand curve. The calculator shows the signed PED and the absolute PED so both views are visible.
What is the difference between PED and |PED|?
PED keeps the sign and shows direction. |PED| removes the sign and is usually the value used to classify demand as elastic, inelastic, or unit elastic.
What does elastic demand mean?
Elastic demand means the absolute value of PED is greater than 1. Quantity demanded changes more than price, so total revenue often moves in the opposite direction of the price change.
What does inelastic demand mean?
Inelastic demand means the absolute value of PED is less than 1. Quantity demanded changes less than price, so total revenue often moves in the same direction as the price change.
What does unit elastic demand mean?
Unit elastic demand means the absolute value of PED is exactly 1. Price and quantity move proportionally, so total revenue is at the turning point.
How does PED affect total revenue?
If demand is elastic, a price increase usually lowers total revenue and a price cut usually raises it. If demand is inelastic, the opposite is usually true.
What if the price change is zero?
PED cannot be calculated because the denominator would be zero. The calculator shows a warning instead of a fake result.
Is this the same as point elasticity?
Not always. The old-and-new-values mode uses midpoint, or arc, elasticity between two points. The linear demand mode calculates point elasticity at one chosen price on a demand curve.
When should I use the direct percentage-change mode?
Use it when the problem already gives the percent change in quantity demanded and the percent change in price. It avoids re-entering old and new values when the percentage changes are already known.
When should I use the linear demand curve mode?
Use it when you have a demand function in the form Q = a - bP and want elasticity at a specific price. The calculator finds quantity at that point and applies the point elasticity formula.
Is arc elasticity the same as midpoint elasticity?
For this calculator, yes. The midpoint method is the standard arc elasticity method for measuring price elasticity of demand between two observed points.
Can price elasticity of demand predict future sales?
It can help screen how sensitive demand appears to be, but it is not a full sales forecast. Competitor behavior, marketing, inventory, seasonality, and the size of the price move can all change the outcome.
